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They shouldn't, if they fit well,but they can lead to blockages if they are too tight, or badly fitted.

Unfortunately most high street shops are atrocious at bra fitting, with mother are being one of the worst.
The same rule apply to fitting nursing bras as normal bras.
Have a look this thebetterbracampaign.blogspot.co.uk/p/fitting-advice.html?m=1 for a guide to how a bra should fit first of all, then you'll know if it's a bra or a fit problem

The bra itself wouldn't cause the engogement, but if it doesn't fit properly it will be uncomfortable.
I second pp advice of betterbracampaign site and measure yourself. Mothercare put me in a 36(!) C when actually I'm a 32 E. Just as an example of their poor fitting service.

Thanks guys, that's really helpful It actually puts me at 30F as opposed to 32E so I'll have to buy even more ridiculously overpriced nursing bras a couple of bigger bras and give them a go!

If anything, you want to err on the side of too big: a cup size bigger won't be too bad for support, but should allow more leeway for the variations in size in a nursing breast. Or measure when you're feeling a bit full!

The website nursingbra-shop.co.uk is really useful, for a big range of sizes, and a chance to try them on for longer than you can in a shop, with easy exchanges.

And I'd be trying to return the others you bought - especially if any are unworn, because they obviously aren't a good fit, despite you being 'fitted'

Good luck!

I had to stop wearing real bras and switch to mothercare stretchy crossover sleep bras because every bra I tried after being measured umpteen times gave me blocked ducts.